Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
852 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator, socle | C23×C43 | C24 |
| Fitting | C43×#391 | C2 |
| hypercenter | #391 | D43 |
| hypocenter | C43 | #2436 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q8×D43 | C2 | semidirect |
| 2. C2×#13063314 | C2 | semidirect |
| 3. C2×#13063313 | C2 | semidirect |
| 5. #14582812 | C2 | semidirect |
| 6. #14582804 | C2 | semidirect |
| 7. #14582777 | C2 | semidirect |
| 8. C4×(C2×D43)⋊C4 | C2 | semidirect |
| 9. C43×#391 | C2 | semidirect |
| 37. C2×Q8×C43 | D4 | semidirect |
| 62. C2×Dic86 | D4 | semidirect |
| 122. C2×D43 | #124 | semidirect |
| 144. #391 | D43 | semidirect |
| 147. C43 | #2436 | semidirect |
| 182. C2×Q8 | D172 | semidirect |